I think you are wise to take hope from the positive signals she sends you, like affection. You also seem to recognize not to make too much out of them or to get your hopes too high. Give yourself some credit - I think you are handling things well.
As for Tuesday, if you want to accept her invitation, then I think you should do so. Remember, there is emotional distance and physical distance. Plus, in the early stages, when the WAS starts reaching out I think it is important to reward that behavior with a positive from the LBS. While one should not appear to be too available, one cannot turn down too many invitations or they may dry up.
Sounds like you have a pretty good handle on things. Keep up the workouts, too!
